## The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected; and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. the first six books, together with the eleventh and twelfth |

### Inni boken

Resultat 1-5 av 79

Side 16

Ax . therefore the remainder AL is equal to the remainder f BG : But it has been

BG , and things that are equal to the same are equal to one another ; therefore

the ...

Ax . therefore the remainder AL is equal to the remainder f BG : But it has been

**shewn**, that BC is equal to BG ; wherefore AL and BC are each of them equal toBG , and things that are equal to the same are equal to one another ; therefore

the ...

Side 28

Book I. ABC would be less than the angle ACB ; but it is not ; there , m fore the

fide AC is not less than AB ; and it has been

AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D.

...

Book I. ABC would be less than the angle ACB ; but it is not ; there , m fore the

fide AC is not less than AB ; and it has been

**shewn**€ 18 , 1 . that it is not equal toAB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D.

...

Side 29

... ED of the triangle CED are greater than CD , add DB so each of these ;

therefore the fides CE , EB are greater than CD , DB ; but it has been

B BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD

, DC .

... ED of the triangle CED are greater than CD , add DB so each of these ;

therefore the fides CE , EB are greater than CD , DB ; but it has been

**shewn**thatB BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD

, DC .

Side 36

...

AGK is equal to GKD ; and they are alternate angles ; therefore AB is parallel b to

CD . Wherefore straight lines , & c . Q.E. D. b 27. 1 , PRO P. XXXI . PRO B. To

draw ...

...

**shewn**that the angle AGK is eK C D qual to the angle GHF ; therefore alsoAGK is equal to GKD ; and they are alternate angles ; therefore AB is parallel b to

CD . Wherefore straight lines , & c . Q.E. D. b 27. 1 , PRO P. XXXI . PRO B. To

draw ...

Side 69

... the same manner it can be

is , F is the center of the circle ABC ; Which was to be found . Cor . From this it is

manifest , that if in a circle a straight line bisect another at right angles , the center

...

... the same manner it can be

**shewn**, that no other point but F is the center ; thatis , F is the center of the circle ABC ; Which was to be found . Cor . From this it is

manifest , that if in a circle a straight line bisect another at right angles , the center

...

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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |

### Vanlige uttrykk og setninger

added alſo altitude angle ABC angle BAC baſe becauſe Book Book XI caſe circle circle ABCD circumference common cone cylinder definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides firſt folid fore four fourth given angle given in poſition given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane produced prop proportionals propoſition pyramid radius rectangle rectangle contained remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſolid ſphere ſquare ſquare of AC Take taken theſe third triangle ABC wherefore whole

### Populære avsnitt

Side 32 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Side 165 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF.

Side 170 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 10 - When several angles are at one point B, any ' one of them is expressed by three letters, of which ' the letter that is at the vertex of the angle, that is, at ' the point in which the straight lines that contain the ' angle meet one another, is put between the other two ' letters, and one of these two is...

Side 55 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Side 32 - ... then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.

Side 45 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 211 - AB shall be at right angles to the plane CK. Let any plane DE pass through AB, and let CE be the common section of the planes DE, CK ; take any point F in CE, from which draw FG in the plane DE at right D angles to CE ; and because AB is , perpendicular to the plane CK, therefore it is also perpendicular to every straight line in that plane meeting it (3.

Side 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 304 - Thus, if B be the extremity of the line AB, or the common extremity of the two lines AB, KB, this extremity is called a point, and has no length : For if it have any, this length must either be part of the length of the line AB, or of the line KB.